The effective capacity of a communications system using unified models is analysed. To obtain a simple closed-form mathematically tractable expression, two different unified approximate models have been used. The mixture gamma distribution which is a highly accurate approximation approach has been first employed to represent the signal-to-noise ratio of fading channel. In the second approach, the mixture of Gaussian distribution which is another unified representation approach has been

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... A comparison between the simulated and numerical results using both distributions over composite a − h − m/gamma fading channels have been provided. Introduction: The ergodic capacity that is proposed by Shannon is measured by assuming no delays for wireless communication systems. Therefore, the effective capacity (or effective rate) has been suggested as a performance metric that can be used to measure the system behaviour under the quality of service restrictions such as system delays [1]. In the effective capacity, guaranteed statistical delay restrictions are assumed to be presented when the maximum constant value of the throughput that arrives at the transmitter is measured. Accordingly, several studies have been devoted to analyse the effective capacity over wireless fading channels [2] . To represent the line-of-sight (LoS), non-LoS, and non-linearity communication scenarios of wireless fading channels, the k − m, h − m, and a − m distributions, which are generalised models that provide better practical results than the traditional distributions such as Nakagami-m are investigated in [3] [4] [5] . The impact of shadowing fading is also considered in the analysis of the effective capacity of communication systems over composite fading channels such as generalised-K and Weibull/gamma [2, 6] . In [7] , the k − m shadowed fading channel which is composite of k − m and Nakagami-m distributions are utilised to model the fading channel. However, no works have been dedicated to analyse the effective capacity over composite h − m/shadowing and a − m/shadowing fading channels. Furthermore, the unified framework in [6] is based on the moment generating function of the instantaneous signal-to-noise ratio (SNR) that cannot be obtained in exact closed-form expression. Motivated by there is no general unified approach for the effective capacity, this Letter provides two different frameworks by using mixture gamma (MG) [8] and a mixture of Gaussian (MoG) distributions [9]. These distributions have been widely utilised in the analysis of digital communication systems [10, 11] . This is because they provide simple closed-form analytic expression of the performance metrics. To this effect, the effective capacity of composite a − h − m/gamma fading condition which is more generalised than the aforementioned channels is analysed using MG and MoG distributions. The main difference between the MG and MoG distributions is the number of the parameters that are required to achieve a minimum mean square (MSE) between the probability density function (PDF) of the exact and approximate models.